J. Phys. Chem. A 2008, 112, 11801–11807
11801
Reaction Electronic Flux: A New Concept To Get Insights into Reaction Mechanisms. Study of Model Symmetric Nucleophilic Substitutions Eleonora Echegaray and Alejandro Toro-Labbe´* Laboratorio de Quı´mica Teo´rica Computacional (QTC), Facultad de Quı´mica, Pontificia UniVersidad Cato´lica de Chile, Casilla 306, Correo 22, Santiago, Chile ReceiVed: June 13, 2008; ReVised Manuscript ReceiVed: September 5, 2008
The present work is focused on studying chlorine and fluorine identity SN2 substitutions on a methyl center, within the framework of the newly introduced reaction electronic flux J(ξ), that allows one to identify charge transfer and polarization mechanisms that take place along the reaction coordinate. The main results concern the discovery of different charge transfer mechanism, despite both reactions have the same energetic pattern with simultaneous bond breaking and formation. It turns out that the chlorine substitution is mainly driven by polarization effects and characterized by through bond interactions while intermolecular charge transfer dominates the fluorine exchange reaction, that is characterized by through space interactions. 1. Introduction Bimolecular nucleophilic substitutions (SN2) at carbon centers are one of the most widely studied reactions in organic chemistry.1 An enormous amount of both experimental2-5 and theoretical6-16 work was focused on extracting the intrinsic reactivity properties of many simple organic systems. Studies of halogen exchange in a methyl center (1), became paradigms for the ion-molecule reactivity study.11,13,16 The one step mechanism presents simultaneous bond breaking and formation at the carbon center, with the classical double well potential and central inversion barrier, due to the formation of stable intermediates: ion-dipole complexes.
X- + CH3X f [X · · · CH3X]- f [X - CH3-X]-‡ f [XCH3 · · · X]- f XCH3 + X- (1) Nowadays, energetic and structural parameters of many SN2 reactions at carbon centers are fully characterized at high theoretical level, for both ab initio14 and density functional theory12,13(DFT). In this context, we present a DFT study of the CH3X + X- (X ) Cl and F) reactions, aimed at recovering electronic structure information in gas phase, in order to analyze important features of the nucleophilic substitution process along the reaction pathway. Conceptual DFT17,18 provides reactivity descriptors of special interest for the study of charge transfer processes, as the chemical potential µ,19-21 which measures the escaping tendency of an electron cloud from an equilibrium system, in consistency with macroscopic thermodynamics. The derivative of µ along the reaction coordinate is the newly introduced reaction electronic flux J(ξ),22 that characterizes electron density rearrangements between the participating precursors in terms of polarization and net charge transfer contributions. In this paper, we used µ and J(ξ) to get insights into the specific interactions that drives the reaction. The paper is organized as follows: Section 2 is devoted to introducing the theoretical descriptors used in characterizing the reactions. Section 3 deals with the computational details, and * To whom correspondence should be addressed.
in section 4, the results are presented and discussed. Section 5 contains some concluding remarks. 2. Theoretical Aspects 2.1. Energy and Force Profile. For any given elementary step of a chemical process, reactants must suffer a series of continuum structural changes to transform into products. The three-dimensional motion of atoms can be condensed to one intrinsic reaction coordinate (IRC)23-25 in which energy is monitored for different structural configurations, generating a minimum energy path, E(ξ), connecting the transition state to reactants and products. The derivative of E(ξ) with respect to the reaction coordinate ξ, is defined as the reaction force,26-28 a global property of the system:
F(ξ) ) -
dE dξ
(2)
The critical points of the reaction force profile are the key points that divides the reaction path in reaction regions, in which different mechanism might be operating in order to keep the reaction going on. These points are a minimum at ξ1 and a maximum at ξ2, thus defining the reactant region within the interval ξR e ξ e ξ1, the transition state region at ξ1 e ξ e ξ2 in which the transition state is located at ξ0 such that F (ξ0) ) 0. The product region is defined between ξ2 e ξ e ξP. This feature set the basis to characterize any property along the IRC within the reaction regions,27-30 and gives insights about specific effects that drives the reaction. In particular, the energy involved in these stages might be quantified trough the amount of work done on the system within the different regions31-34
W1 ) -
∫ξξ F(ξ) dξ
(3)
W2 ) -
∫ξξ F(ξ) dξ
(4)
1
R
0
1
such that the energy barrier is ∆E‡ ) W1 + W2. The nature of W1 is mainly associated with preparative structural changes,28,34 whereas W2 has been attributed to electronic effects, since at the transition state region,28,31 electronic properties dramatically changes thus indicating that the electron density is being redistributed along the new atomic connectivity, envisioning
10.1021/jp805225e CCC: $40.75 2008 American Chemical Society Published on Web 10/23/2008
11802 J. Phys. Chem. A, Vol. 112, No. 46, 2008
Echegaray and Toro-Labbe´
product formation.28,33 Although these conclusions might differ between chemical reactions, they enlightens us to search for structural and electronic parameters that can point out how and where electron transfer is taking place and which are the main factors that contribute to the reaction activation barrier, that is to say, to the reaction mechanism. 2.2. Chemical Potential and Reaction Electronic Flux (REF). From DFT variational minimization of the energy functional, the associated Lagrange multiplier is identified with the chemical potential µ ) (∂E/∂N)ν(r), first order response of the energy to changes in the number of particles.19,20 Despite we are not dealing with open systems, the measure of the escaping tendency of the whole electronic cloud is of great value for understanding the electron transfer processes during a chemical reaction. Numerical values of chemical potential are obtained using the finite difference approximation followed by the Koopmans Theorem,35 thus giving approximate expressions for µ17-20
1 1 µ ≈ - (I + A) ≈ (εH + εL) 2 2
(5)
where I is the first ionization potential, A is the electron affinity, and εH and εL are the energies of the highest occupied and lowest unoccupied molecular orbitals, HOMO and LUMO, respectively. The continuous variation of the chemical potential is followed along the reaction pathway, through infinitesimal changes for the series of non stationary points that comprises the IRC. The reaction electronic flux is then defined as the negative of the chemical potential gradient, with transport coefficient Q22
( dµdξ )
J(ξ) ) -Q
(6)
The development of this formulation is presented in previous studies of the energy dependence to changes in µ and η, E{µ, η},26,36 where an analytic expression for the transport coefficient Q is made available for specific cases in which the energy and the chemical potential present an important degree of correlation.26 The characterization of electronic transport coefficients within the frame of the reaction electronic flux is an open issue that will be addressed elsewhere. In this paper Q ) 1 will be used to focus the analysis on the derivative of the chemical potential only. Making the analogy with the free energy in macroscopic thermodynamic, eq 6 indicates that a positive reaction electronic flux will entail spontaneous changes in the electronic density, whereas negative J(ξ) values are related with non spontaneous electronic reordering. Going deeper into the macroscopic thermodynamics analogy, we can expect that during bond formation between reactants of different chemical potential µA > µB, there will occur an electron density transfer from A to B in order to stabilize the system and to fulfill µA ) µB at equilibrium. This transfer can be analyzed through the decomposition of the total reaction electronic flux J(ξ), into intra and intermolecular electronic contributions, characterized in terms of polarization effects Jp on each reactant and net charge transfer processes Jt between them
J(ξ) ) Jp(ξ) + Jt(ξ)
(7)
Jp(ξ) ) JA(ξ) + JB(ξ)
(8)
where
The polarization flux Jp(ξ) split into two contributions associated to the specific fragments involved in the reaction, as indicated by eq 8, will be determined through the use of the counterpoise37-39
Figure 1. Energetic sketch for a generic SN2 reaction: XCH3 + X-.
method, designed for characterizing the basis set superposition error in molecular interactions within the supermolecule approach. Assuming that the fragmentation of the supermolecule holds all along the reaction coordinate, it is possible to obtain the chemical potential for the reaction participants at each point along the reaction coordinate. This provides a way to estimate the polarization fluxes JA(ξ) and JB(ξ) induced in fragments A and B by the presence of fragments B and A, respectively. In this way, the REF decomposition emerges as a powerful tool to discover charge transfer and polarization effects that are involved in the mechanism of chemical reactions. 3. Computational Details AllcalculationswereperformedattheB3LYP/6-311++g**40-43 theory level, using the standard Gaussian 0344 package. The characteristic SN2 collinear attack was ensured fixing the X-C-X angle at 180° during the transition state optimization, and the reaction path was followed by an IRC24,25 type calculation in mass weighted internal coordinates45 (ξ is given in amu1/2 bohr), between the two ion-dipole complexes, RC and PC (Figure 1). For the specific cases studied here, the efficiency of the B3LYP hybrid functional to provide reliable reaction barriers was tested by making calculations using the functionals PBEPBE46 and MPWPBE,46,47 the results obtained using the standard 6-311++g** basis set were also compared with the reference CCSD(T) calculations by Schaefer et al.14 For R1 the B3LYP barrier (8.42 kcal/mol) compares quite well with the coupled cluster calculation (8.13 kcal/mol), whereas the PBEPBE and MPWPBE calculations clearly underestimate the barrier (6.52 and 6.35 kcal/mol, respectively). Although in R2 the three density functionals underestimate the CCSD(T) energy barrier (13.11 kcal/mol), the B3LYP functional (9.54 kcal/mol) still provides the best comparison; PBEPBE (6.55 kcal/mol) and MPWPBE (6.48 kcal/mol) values differ by a factor of 2 with respect to the reference CCSD(T) result. Single-points calculations were performed at the already optimized IRC geometries in order to obtain energetic and electronic data, as well as εH and εL values to calculate the chemical potential µ as indicated by the Koopmans theorem. It has been shown that, although the Koopmans theorem is defined
Reaction Electronic Flux
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TABLE 1: Energetic Parameters in kcal/mol for R1, ClCH3 + Cl-, and R2, FCH3 + FR1 R2
∆EC
∆E‡
W1
%W1/∆E‡
∆µ‡
-9.93 -14.52
8.43 9.55
4.59 5.22
55% 55%
-16.44 -17.59
within the frame of the Hartree-Fock methodology, it can be applied to DFT calculations.48-50 Studies on a variety of systems show that chemical potentials determined using the energy of the frontier molecular orbitals or the ionization potentials and electron affinities, present similar trends48,51,52 so that it is expected that the derivative should not be affected by the use of either way of eq 5. The counterpoise37 routine was employed to calculate the polarization contribution to the REF from each of the reaction participants A ) X1CH3 and B ) X2-, as indicated by eq 8. 4. Results and Discussion 4.1. Energy and Reaction Force Profiles. The first energetic parameter analyzed is the binding energy ∆EC of the ion-dipole complexes RC (Figure 1), as a measure of the X-C bond strength regarding the separated reactants. A stronger interaction for the fluorine (Table 1) is reported, about 4.5 kcal/mol above the chlorine complexation energy. This result can be attributed to the higher electronegativity and smaller size of the fluorine atom, allowing an stronger electrostatic interaction with the molecular fragment.53,54 From RC, the reaction follows a symmetrical path leading to the product ion-dipole complex PC, surmounting the reaction activation barrier ∆E‡ (Table 1). The selectivity toward the halogen atom is lost, differing by about 1.1 kcal/mol between the chlorine reaction R1 and the fluorine reaction R2 (eq 1). As both reactions are symmetric (simultaneous bond breaking and formation), the thermodynamic factors related to the energy of broken and formed bonds are canceled for each process; therefore, the reaction activation barrier does not reflect the particular affinity of the carbon center for any of the two halogen atoms. Some other important contributions to the barrier height are the structural stress of the central carbon fragment55 and the steric repulsion between it and the entering nucleophile;56 which are equivalent for R1 and R2 since the same methyl center is considered. Energy and reaction force profiles are comparatively presented in Figure 2 for R1 and R2. The critical points ξ1 and ξ2 (dashed vertical lines in the reaction force profiles), define the reaction regions that will frame our study, allowing the energetic barrier decomposition in terms of the work invested in each region, in order to reach the highly delocalized transition structure. Values of W1 are reported in Table 1, showing that the energetic weight of W1 upon the activation barrier is the same for both reactions, a 55% of each ∆E‡. Despite the differences in the RC initial bond strength, R1 and R2 have the same energetic degree of advance at ξ1. An initial slope analysis of the reaction force profile, shows the evolution of the forces opposing the preparation step in the reactants region, denoting a change in the nature of the C · · · X2 bond. As described in the introduction, the SN2 structural mechanism is a collinear attack, in which the main feature is the carbon-halogen interatomic distance. Figure 3 displays the evolution of the X1-CH3 and X1CH3 · · · X2 distances along the reaction coordinate ξ for both processes. The most noticeable feature is that as the nucleophile approaches to the methyl center, after a preparative stage where the X1-CH3 bond distance does not change, the leaving group goes away reaching the same rate of the incoming atom. The preparative stage last until a
Figure 2. Energy and force profiles for R1, ClCH3 + Cl-, and R2, FCH3 + F-. The reaction coordinate ξ is given in amu1/2bohr.
Figure 3. Halide-carbon atomic distance profiles R1 and R2.
certain nucleophile proximity, 1.88 Å at ξ ≈ -3.2 for R1 and 1.48 Å at ξ ≈ -2.5 for R2 (shown by arrows in Figure 3). In a first approximation to the electronic structure study, dipole moment (DM) profiles along the IRC provide a balanced vision of both structural and electronic reorders, reflecting the
11804 J. Phys. Chem. A, Vol. 112, No. 46, 2008
Figure 4. Dipole moment profiles for R1 and R2.
Figure 5. Chemical potential and electronic flux profiles for R1 and R2.
evolution of the molecular charge distribution (Figure 4). Three main features stand out: a higher DM initial value for R1, about 2 D above R2, in accordance with a less strong binding energy ∆EC; a slope discontinuity in the reactant region at the same reaction coordinate observed in the reaction force and bond distance profiles (ξa1 ) (3.2 and ξa2 ) (2.5); and a fast charge equalization in the transition state region in order to reach DM(TS) ) 0, due to the symmetrical distribution of the electron density along the X1-C-X2 axis. From now on, in order to simplify further analysis, the reaction coordinate corresponding to the activation inflection points will be referred as ξa1 for R1 and ξa2 for R2. 4.2. Chemical Potential and Reaction Electronic Flux. 4.2.1. General Features of the µ(ξ) and J(ξ) Profiles. Moving forward on the electronic structure analysis, Figure 5 shows, in a comparative way, the chemical potential profile for R1 and R2, relative to reactants. The changes between RC and the transition state (∆µ‡) are very significative, about -17 kcal/ mol each (Table 1). This implies that the TS configuration has lower electron escaping tendency, a measure of the stability of
Echegaray and Toro-Labbe´ the highly delocalized electronic cloud. There is no significant difference between the ∆µ‡ barriers for R1 and R2, characterizing general features of the methyl halide substitution. Relative to the initial slopes of the curves, once again there is evidence of an activation process in the reactant region, that after ξa1 and ξa2, breaks out a rapid electron cloud redistribution in the TS region, just as in the DM profile. In order to explore in depth the electron redistribution caused by the chemical potential equalization, the REF profile J(ξ) is analyzed (Figure 5), producing interesting results. R1 has no flux during the first part of the reactant region (from RC to ξa1), providing evidence for a strictly electrostatic interaction between the halogen atom and the methyl-halide fragment. In contrast, R2 presents a small basal electronic flux (from RC to ξa2), which is consistent with a higher complexation energy ∆EC, due to a stronger X2 · · · C bond in the reactive complex. In a second instance, once each nucleophile reaches ξa1 and ξa2, both reactions are activated by an important reaction electronic flux, which allows to overcome the preparative stage in order to initiate the simultaneous bond breaking and formation process. R1 reaches a single maximum in the TS region, whereas R2 features an incipient shoulder before ξ1 and a maximum after ξ1, as a first evidence of different charge distribution mechanisms, attributable to different initial bond strength and/or nature. It has been established that the reaction coordinate segmentation given by the force profile clearly frames the activation phenomena in the reactant region, showing that its energetic cost is proportionally equivalent for R1 and R2 (a 55% of each barrier). If we consider the different initial binding energies ∆EC, it is reasonable to expect dissimilar charge transfer mechanism, in order to minimize the energetic expense of the monovalent anion exchange. The REF decomposition, together with an NBO analysis will enlighten this fact. Aside, it is important to point out that the TS geometry gathers some special features, becoming a balance point: despite being thermodynamically unstable, the electronic properties are equilibrated with the reaction driving forces, characterized by F(ξ0) ) 0, DM(ξ0) ) 0 and J(ξ0) ) 0. 4.2.2. REF Decomposition. The REF decomposition shows different charge distribution mechanism for the two studied reactions. In Figure 6 the results are presented comparatively in terms of polarization effects Jp(ξ) on each reactant and net charge transfer processes between them Jt(ξ), along with the total flux J(ξ). Due to the reaction symmetry and for the sake of an enhanced information display, the profiles are presented from the reaction complex RC to the transition state coordinate only. For the chlorine substitution R1, it is found that the zero flux region observed in the J(ξ) profile is not the consequence of a cancelation between Jp(ξ) and Jt(ξ), but a genuine electrostatic interaction region. As the nucleophile approaches, once a certain Cl1CH3 · · · Cl2 distance of 2.8 Å is reached, a rapid polarization flux Jp(ξ) emerges, presenting its maximum at ξ ) -2.3, a few steps after ξa1, then Jp(ξ) is sustained along the transition state region, generating intramolecular charge redistribution until the TS configuration. The polarization flux activates an initially non spontaneous transfer flux Jt(ξ) < 0, that increases constantly in order to reach its maximum around ξ ) -1.29, corresponding to the maximum of J(ξ). The maximum REF observed at the transition state region is due, in almost the same extent, to polarization and transfer effects. At the TS configuration the zero flux is attained by cancelation of the two contributions Jp(ξ) and Jt(ξ).
Reaction Electronic Flux
Figure 6. Electronic flux decomposition profiles for R1 and R2. The electronic flux is given in kcal/mol · ξ.
A different behavior of the REF is observed for the fluorine substitution R2. The small positive (spontaneous) reaction electron flux present since the reactive complex formation corresponds to pure transference flux, generating a much more strong bond for the reactive complex RC, than the corresponding purely electrostatic one. The nucleophile approach enhances this interaction, rising the transference flux considerably after ξa2, reaching a first maximum as it approaches to ξ1. The REF incipient shoulder is therefore mostly due to electron transfer effects. At the same time, Jt(ξ) activates a polarization response Jp(ξ) which is completed in the transition state region. This internal charge redistribution phenomena is accompanied by a new local maximum in Jt(ξ), corresponding to the second hump in the J(ξ) profile which in turn is now mostly due to polarization effects. Both components of the REF tend to decrease toward the TS geometry, showing that the major electronic rearrangements were completed in the first part of the TS region. 4.2.3. Natural Population Analysis. Figure 7 displays the natural charge profiles for the three main atomic centers on each reaction, adding some valuable information in order to support the electronic flux decomposition. Consistently with our previous observations, the charge profiles exhibit activation inflection points at ξa1 and ξa2. In the R1 profile, initial atomic charge values remain constant until ξa1, confirming purely electrostatic interactions in the first half of the reactants region. Afterward, the REF break out symmetric charge equalization between the entering and leaving halide, passing by a crossing point in the TS: maximum charge delocalization is reached in the equally distanced bonds, framing the major electronic reorders into the TS region. By observing the ratio of the halogens to the carbon center charge, it is possible to conclude some features about the reaction bond nature. Initially, the carbon charge is framed
J. Phys. Chem. A, Vol. 112, No. 46, 2008 11805
Figure 7. NPA charge profiles for R1 and R2.
TABLE 2: NPA and NBO Parameters for R1, Atomic Charges and Bond Populations RC ξa1 ξ1 TS
C
Cl1
Cl2
σ1
σ1*
nCl2
σ2
-0.492 -0.496 -0.423 -0.365
-0.190 -0.217 -0.366 -0.613
-0.963 -0.934 -0.840 -0.633
1.996 1.996 1.995 1.996
0.038 0.064 0.156 0.351
1.964 1.935 1.841 1.634
σ2*
TABLE 3: NPA and NBO Parameters for R2, Atomic Charges and Bond Populations RC ξa2 ξ1 TS
C
F1
F2
σ1
-0.092 -0.097 -0.085 -0.079
-0.470 -0.492 -0.580 -0.702
-0.955 -0.923 -0.839 -0.713
1.997 1.996 1.994 1.887
σ1*
nF2
σ2
σ2*
0.041 1.960 0.067 1.928 0.147 1.841 0.182 1.884 0.179
between the chlorines charge, revealing covalent bond interaction. The carbon-halide bond in the chloromethane moiety is characterized by an extensive density overlap, with a high negative charge on the carbon -0.492 and a low charge value of -0.190 on the chlorine (Table 2). Once the transition state is reached, the ratio changes because the carbon charge has been decreased up to -0.365, while both halogens charge lie under this value, suggesting that certain ionic character emerges. At the same time, the charge evolution of the carbon center along the reaction coordinate enlightens the substitution interactions, showing sensibility to the nucleophile exchange. As the electron transfer is activated, the NPA charges are affected, reflecting the predominance of through bond interactions57 within the charge transfer mechanism. In terms of the REF, the sudden polarization of the methyl halide fragment (Jp(ξ) rise), activates the initially non spontaneous (Jt(ξ) < 0) transference flux between the substitution participants, responsible for the partial (and
11806 J. Phys. Chem. A, Vol. 112, No. 46, 2008 symmetric) bond breaking and formation process. These reorders are reflected in the gradual carbon center charge loss, acting as a bridge between the two partially bonded chlorine atoms. After the Jt(ξ) max, the polarization flux is responsible for the electron density redistribution, in order to attain a highly delocalized transition structure. The R2 NPA profile shares general features with the R1 profile: the entering and leaving halide present a characteristic SN2 symmetric charge evolution with respect to the transition state, activated in the reactants region (ξa2) and mainly located in the TS region. However, a distinctive feature of reaction R2 is found on the carbon charge and its evolution. Initially it is not framed between the fluorines charges, but above them with a small value of -0.092 (practically neutral), reflecting the ionic character of the methyl-halide bond. This charge value will remain practically constant during the substitution process (Table 3), as a sign of through space57 interactions in order to achieve the charge equalization. As the entering halogen approaches, a partial bond starts to develop with the molecular fragment, generating the first Jt(ξ) maximum. Note that the fluorine is a small atom, so the transfer phenomena precedes the polarization one: at the first Jt(ξ) max Jp(ξ) start to rise, completing the density delocalization along the X-C-X axis. In the simultaneous bond breaking and formation, through space interactions must predominate, otherwise, the charge on the carbon center will reflect a partial accumulation or depletion, as it did in the R1 profile. 4.2.4. Natural Bond Orbital Analysis. It results very interesting to contrast the REF study with the classical chemical picture provided by the NBO bond analysis.58 The electronic structure of the studied compounds is rationalized in terms of a Lewis type bond net, where localizing bonds (σ) and lone pairs (n) are basic units for molecular assembly. Antibonding orbitals (σ*) are used to describe non covalent effects and Rydberg orbitals (ry) for delocalization effects, representing unused valence shell capacity. As for the NPA, the bond evolution was followed all along the reaction pathway. Tables 2 and 3 displays the main results for the critical points of the reaction profile: reactants (RC), ξa, ξ1, and TS geometry. The RC configuration of R1, presents a proper covalent bond σ1 (Figure 8), and its corresponding antibond σ1*, with an occupation number of 0.038, provided trough an interaction with the entering chlorine Cl2 lone pair, a 3p orbital with its population decreased to 1.964. As the reaction moves forward on the reactant region, the outbreak of the reaction electronic flux occurs in ξa1 which is characterized by the first interaction from the molecular fragment σ1 to a delocalized Rydberg orbital of the Cl2 nucleophile. Despite being a really small interaction (0.004 transferred), it marks the beginning of a deeper rapport of the electronic clouds, with a retrodonation phenomena that will remain until the TS configuration. After ξa1, Jp reaches its maximum value at ξ ≈ -2.7, coinciding with the appearance of charge transfer from σ1 and σ1* orbitals to delocalized ry* orbitals on the chlorine and carbon atoms that form the corresponding bond. The charge density is redistributed in the chloromethane moiety in order to prepare the leaving group, reflecting the connection between the reaction polarization flux Jp and internal charge transfer processes, confirming through bond polarization in order to delocalize the transferred charge. On the other hand, the charge transfer from the lone pair to the antibonding σ1* increases continuously, while the σ1 population remains constant at 1.995, showing that the σ1* is populated completely from the entering lone pair.
Echegaray and Toro-Labbe´
Figure 8. Transition state bond sketches, R1 and R2.
Finally, in the transition state configuration no proper C-Cl2 bond is generated (σ2), explaining the steady polarization phenomena observed in Figure 6, in order to delocalize the charge coming from the nCl2 f σ1* transfer. Noncovalent effects are enhanced, reflecting a growing ionic character in the bond evolution, in agreement with our previous observations on the R1 charge profile. This behavior might be attributed to a high electronegativity and chlorine size, capable of retaining much more electron density than the compared fluorine anion. The fluorine substitution presents the same initial bond net than the chlorine one. The ion-dipole complex is formed by an nF2 f σ1* interaction, toward the fluoromethane moiety, with an small charge transfer of 0.041. As the reaction moves forward, once again the activation point ξa2 coincides with the establishment of retrodonations from the molecular fragment to the entering fluorine F2, a σCH f ryF2* interaction, involving this time the three C-H bonds instead of only the σ1 bond in R1, illustrating the through space interaction pattern. The distinctive R2 reaction feature occurs at the Jt(ξ) second maximum, which exactly coincides with the formation of a new bond between the entering fluorine and the molecular fragment, generating a pentacoordinate carbon center. Before reaching the transition state and after ξ1, the preexistent σ1 bond has a small population decrease to 1.918, while the nF2 transfers its population to the new σ2 bond to reach 1.861. From this point on, the main feature will be an electron delocalization processes through σ1 f σ2* crossed charge transfer to attain the equally populated σ1 and σ2 bonds, enhancing the ionic character of the transition state configuration. Aside, if we compare the R1 and R2 nX2 populations at ξ1, the same value is encountered 1.841 (Tables 2 and 3), along with a revealing feature: at this point the σ1 f σ1* interactions are established for the first time in both reactions. If we recall that the energetic degree of advance was equivalent at the same point (55% of ∆E‡), we can attribute this energy investment to the population decrease of the entering lone pair nX2 from 1.996 to 1.841 in both reactions. The structural rearrangements observed in Figure 3 appear clearly related to the electronic transfer and its energetic cost: despite having a different charge transfer mechanism, common features relates both processes, implying that reaction peculiarity is mostly developed in the transition state region. 5. Concluding Remarks The concerted SN2 mechanism is recovered for the chlorine and fluorine identity reactions. Bond distances and atomic charges evolve symmetrically, generating an equivalent energetic pattern that goes from ion-dipole complexes to a highly delocalized transition structure, characterized by a minimum ‡ , DM ) 0). In this context, electron escaping tendency (∆µmin the reaction coordinate segmentation, provided by the reaction force analysis, shows to be an unambiguous and natural way to elucidate the reaction mechanism. For both processes, the reaction activation occurs in the reactants region and it is related with structural parameters (entering nucleophile proximity), along with a peculiar electronic density response in each case: the reaction electronic flux and
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